Question

Two lines have the given equations. Use the Linear Combination Method to solve.

Answer 1

`\large{\textbf{(x,y) = (-7, -15)}\\}`

Explanation:

`\large{\textup{The given equations represent two straight lines.}}\\\\ \large{\textup{To solve them is to find the \textbf{point of intersection} of the two lines.}}\\`

`\begin{align*}\\2x - y &= 1  \hspace{25mm} (1) \\3x - y &= -6 \hspace{24mm} (2) \\\end{align*}`

`\large{ \textup{We start by eliminating one variable.}}\\`

`\textup{In this case, $y$ can be eliminated by subtracting (1) \& (2).}}}`

`\large{\textup{We get}\\}`

`\begin{align*}2x - y &= 1   \\-3x + y &= 6 \\\implies -x &= 7\\\implies x &= -7\end{align*}`

`\large{\textup{Substituting $x = -7$ in $(1)$, we get:}$ 2(-7) - 1 = y \\ $$\implies y = -15 $\\\textup{Therefore, $x= -7, y = -15$}\\\textup{Simply put, $(x,y) = (-7,-15) $ is the point of intersection of $(1)$ \& $(2)$}.}`